Question

Need equation of the ellipse with vertices at (-25, 0), (25, 0) and co-vertices (0, -15), (0, 15)?

Answer 1

Standard equation of horizontal ellipse is (x-h)^2/a^2+(y-k)^2/b^2 = 1

a > b

Given vertices

(h+a,k) = (25,0)

(h-a,k) = (-25,0)

Covertices

(h,k+b) = (0,15)

(h,k-b) = (0,-15)

From above values we can able to write a = 25, b = 15

(h,k) = (0,0)

Substiue the above values in Standard equation of horizontal ellipse.

(x-0)^2/25^2+(y-0)^2/15^2

x^2/625+y^2/225 = 1